4.21 A municipal bus company has started operations in a new subdivision. Records were kept on the numbers of riders on one bus route during the early-morning weekday service. The accompanying table shows proportions over all weekdays.

Number of riders 20 21 22 23 24 25 26 27 Proportion 0.02 0.12 0.23 0.31 0.19 0.08 0.03 0.02

a. Graph the probability distribution.

b. Calculate and graph the cumulative probability distribution.

c. What is the probability that on a randomly chosen weekday there will be at least 24 riders from the subdivision on this service?

d. Two weekdays are chosen at random. What is the probability that on both of these days there will be fewer than 23 riders from the subdivision on this service?

e. Find the mean and standard deviation of the number of riders from this subdivision on this service on a weekday.

f. If the cost of a ride is $1.50, find the mean and standard deviation of the total payments of riders from this subdivision on this service on a weekday.